Past Events
A friendly introduction to everyone's favourite badly-approximable irrational, featuring symplectic topology and J-holomorphic curves.
We will discuss how Atiyah-Singer index theorem implies the Riemann-Roch theorem of complex manifolds, the Hirzebruch signature theorem of 4n-dimensional manifolds and the Rokhlin theorem of spin 4-manifolds.
Abstract:
Discrete (resp. Brownian) loop soups are random collections of loops on graphs (resp. in the continuum) defined as Poisson point processes with the intensity measure given by what is known as the discrete (resp. Brownian) loop soup measure. In the discrete setting, we will…
Abstract
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex with a latent feature vector sampled from a mixture of Gaussians, and we add edge if and only if the feature vectors…
In joint work with Marco Marengon we present a simple but flexible
method to simultaneously remove multiple double points of immersed
surfaces in 4-manifolds. One consequence is that in an appropriate
sense many knots bound disks in 4-manifolds, and in particular, we
…
In 1987, Harris and Vickers [HV87] proposed a model of a race in which two firms invest resources, each trying to be the first to secure a patent. They called the model tug of war. A counter moves randomly left or right on an integer interval, with the odds of a rightward move at each turn…
In this talk, we will discuss the proof of irrationality of 2-adic zeta value at 5. It uses an arithmetic holonomicity theorem, which can be viewed as a refinement of André’s algebraicity criterion and has also been studied in the recent work of Bost and Charles. We will also discuss some other…
What is a black hole, and how can we draw them? We can answer this question with Penrose diagrams, which are used in general relativity to depict geometric features of spacetime. We will then explore the relation between this underlying geometry and the behaviour of solutions to wave equations…
Abstract:
We introduce the Sherrington-Kirkpatrick model, describing the link between its free energy and Gibbs measure, the "cavity computation," and the replica method. In doing so, we will cover several useful techniques -- Gaussian integration by parts, continuous approximation…